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The parallel axis theorem relates Icm, the moment of inertia of an object about an axis passing through its center of mass, to Ip, the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is Ip=Icm+Md2, where d is the perpendicular distance from the center of mass to the axis that passes through point p, and M is the mass of the object. Part A Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Icm=112mL2.

Required:
Find Iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod.

Respuesta :

Answer:

  I = ⅓ m L²

Explanation:

They tell us to use the parallel axes theorem

         I = [tex]I_{cm}[/tex] + M d²

The moment of inertia of a rod with respect to the center of mass is

         I_{cm} = [tex]\frac{1}{12}[/tex]  m L²

the distance from the center of mass that coincides with its geometric center to the ends of the rod is

         d = L / 2

we substitute

       I =[tex]\frac{1}{12}[/tex]  m L² + m (L/2)²

       I = m L² (  [tex]\frac{1}{12} + \frac{1}{4}[/tex] )

       I = m L² ( [tex]\frac{1+3}{12}[/tex] )

       I = ⅓ m L²

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